Question

22. A husband and a wife apprear in an interview for two vacancies for the same post.The probability of husband's selection is 3÷5 and that of wife's selection is 1÷5. Find the probability that:

(i) both are selected
2) exactly one is selected
3) none is selected​

Answer 1

`P(Both) = (3)/(25)`

`P(One) = (12)/(25)`

`P(None) = (22)/(25)`

Explanation:

Given

`P(H) = (3)/(5)`

`P(W) = (1)/(5)`

Solving (a): Both selected

`P(Both) = P(H) * P(W)`

`P(Both) = (3)/(5) * (1)/(5)`

`P(Both) = (3)/(25)`

Solving (b): One selected.

This event can be represented as: HW' or H'W

So:

`P(One) = P(H) * P(W') + P(H') * P(W)`

Where:

P(W') = 1 - P(W) and P(H') = 1 - P(H).

So:

`P(One) = (3)/(5) * (4)/(5) + (2)/(5) * (1)/(5)`

`P(One) = (12)/(25) + (2)/(25)`

`P(One) = (12)/(25)`

Solving (c): None selected.

This is the complement of (a) above.

i.e.

`P(None) = 1 - P(Both)`

`P(None) = 1 - (3)/(25)`

`P(None) = (25 - 3)/(25)`

`P(None) = (22)/(25)`